Title:

Exploratory lattice QCD studies of rare kaon decays

The rare kaon decays K → πl^{+}l^{} and K → πνν proceed via flavour changing neutral currents, and are thus heavily suppressed in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential new physics. These decays first arise as secondorder electroweak processes, hence we are required to evaluate fourpoint correlation functions involving two effective operators. The evaluation of such fourpoint correlation functions presents two key difficulties: the appearance of unphysical terms in Euclideanspace correlators that grow exponentially as the operators are separated, and the presence of ultraviolet divergences as the operators approach each other. I present the results of the first exploratory studies of the calculation of the longdistance contributions to these decays using lattice QCD. The decays K → πl^{+}l^{} are completely longdistance dominated; this lattice calculation is thus the first step in providing abinitio estimates for the amplitudes of these decays. Our simulations are performed using the 24^{3 }x 64 domain wall fermion ensemble of the RBCUKQCD collaboration, with a pion mass of 430(2)MeV, a kaon mass of 625(2)MeV, and a valence charm mass of 543(13)MeV. In particular we determine the form factor, V (z), of the K^{+} (k) → π^{+} (p) l^{+}l^{} decay from the lattice at small values of z = q^{2}=M^{2}_{K} (where q = k  p), obtaining V (z) = 1.37(36); 0.68(39); 0.96(64) for the three values of z = 0.5594(12), 1.0530(34), 1.4653(82) respectively. The decays K^{+} → π^{+}νν are shortdistance dominated, although the longdistance contributions represent significant sources of uncertainty. The lattice calculation of the decay amplitudes is made particularly difficult by the presence of ultraviolet divergences in the fourpoint correlators. I present the calculation of the renormalised decay amplitudes, using the 16^{3}x32 domain wall fermion ensemble of the RBCUKQCD collaboration, with a pion mass of 421(1)(7)MeV, a kaon mass of 563(1)(9)MeV, and a valence charm mass of 863(24)MeV. In particular we find the difference between the perturbative and lattice estimates of the charm contribution to these decays to be ΔP_{c} = 0.0040(13)(32)(45).
